Fixed rate drug delivery pumps have typically utilized a metal bellows reservoir with a two-phase propellant to keep the drug at a constant pressure of approximately 36 p.s.i. The drug flows out of the reservoir through a flow restrictor, such as a glass capillary tube that has been calibrated to produce the desired flow rate. Fixed rate pumps are typically 80 cc to 100 cc in size. The reservoir utilizes a metal bellows that is made out of suitable metal such as titanium. However, such metal bellows typically are not very elastic and the reservoir needs to be relatively large in size to accommodate the accordion leaves. Such a construction has prevented the design of a smaller pump and is expensive. The present invention addresses the problems associated with the prior art pumps and may be utilized in either a fixed rate or a variable rate smaller sized pump for the delivery of drugs.